{"paper":{"title":"Transformations of polar Grassmannians preserving certain intersecting relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Kaishun Wang, Mark Pankov, Wen Liu","submitted_at":"2013-07-09T01:28:04Z","abstract_excerpt":"Let $\\Pi$ be a polar space of rank $n\\ge 3$. Denote by ${\\mathcal G}_{k}(\\Pi)$ the polar Grassmannian formed by singular subspaces of $\\Pi$ whose projective dimension is equal to $k$. Suppose that $k$ is an integer not greater than $n-2$ and consider the relation ${\\mathfrak R}_{i,j}$, $0\\le i\\le j\\le k+1$ formed by all pairs $(X,Y)\\in {\\mathcal G}_{k}(\\Pi)\\times {\\mathcal G}_{k}(\\Pi)$ such that $\\dim_{p}(X^{\\perp}\\cap Y)=k-i$ and $\\dim_{p} (X\\cap Y)=k-j$ ($X^{\\perp}$ consists of all points of $\\Pi$ collinear to every point of $X$). We show that every bijective transformation of ${\\mathcal G}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2316","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}